Document Type : Original Manuscript

Author

Department of Mathematics, MVGR College of Engineering, P.O. Box 535004, Vizianagaram, Andhra Pradesh, India.

10.22044/jas.2022.11321.1565

Abstract

The concepts of intrinsic ideals and inlets are introduced in a distributive lattice. Intrinsic ideals are also characterized with the help of inlets. Certain equivalent conditions are given for an ideal of a distributive lattice to become intrinsic. Some equivalent conditions are derived for the quotient lattice, with respect to a congruence, to become a Boolean algebra. Some topological properties of the prime spectrum of intrinsic ideals of distributive lattice are derived.

Keywords

###### ##### References
1. G. Birkhoff, Lattice theory, Amer. Math. Soc. Colloq. XXV, Providence, U.S.A., 1967.
2. T. S. Blyth, Ideals and filters of pseudo-complemented semilattices, Proc. Edinburgh Math. Soc., 23 (1980), 301–316.
3. S. Burris and H. P. Sankappanavar, A Cource in Univerasal Algebra, Springer Verlag, 1981.
4. W.H. Cornish, Annulets and α-ideals in distributive lattices, J. Aust. Math. Soc., 15 (1973), 70–77.
5. W. H. Cornish, Normal lattices, J. Aust. Math. Soc., 14 (1972), 200–215.
6. W. H. Cornish, Quasicomplemented lattices, Comment. Math. Univ. Carolin., 15(3) (1974), 501–ff511.
7. A. P. Phaneendra Kumar, M. Sambasiva Rao, and K. Sobhan Babu, Generalized prime D-filters of distributive lattices, Arch. Math., 57(3) (2021), 157–174.
8. M. Sambasiva Rao, e-filters of MS-algebras, Acta Math. Sci. Ser. B, 33(3) (2013), 738–746.
9. T. P. Speed, Some remarks on a class of distributive lattices, J. Aust. Math. Soc., 9 (1969), 289–296.